1. Field of the Invention
This invention relates to migration of seismic data and in particular to migration of diving wave reflections characterized by dips that exceed 90.degree..
2. Related Art
As is well known, the propagation velocity of a seismic wavefield through the earth usually increases with increasing depth. The velocity gradient can be attributed to some extent to increased rock compaction because of the increase in static loading of the overlying strata. Additional factors affecting velocity involve rock type, composition, texture, chemistry and orogeny. Commonly, each stratum of the earth is characterized by a velocity that is higher than the velocity of the stratum above it although velocity reversals are known. Thus, the wavefield propagation velocity increases stepwise with depth. The stepwise velocity/depth function can often be approximated by a smooth curve.
A wavefield emanating from a seismic source will propagate downwards into the earth, radiating uniformly in all directions assuming a homogeneous laterally isotropic earth. Assuming also closely-spaced substantially flat-dipping strata, a normally-incident, zero-offset wavefield ray will be reflected from the respective strata and return to the surface as a plurality of reflected events whose travel times are a function of the depths of the strata from which the wavefield was reflected. At angles other than normal incidence, the wavefield ray paths will be curved due to refraction at the interfaces between the successive earth layers. Thus, the trajectory of the wavefield from a source to a receiver after reflection from a subsurface stratum will include a downgoing incident segment and an upgoing reflected segment, both of which will follow a curved path. The amount of ray-path curvature depends upon the steepness of the velocity gradient as a function of depth to the reflecting stratum and the offset between source and receiver. In the presence of a region characterized by a steep velocity gradient, the downgoing component of the ray path trajectory may be reversed and bent back to the surface with no appreciable travel path through a distinctive refractor. The ray path is turned upwards before nominal reflection occurs. It is within the realm of possibility that an upwardly-refracted wavefield will encounter an obstruction, such as a horizontally projecting salt dome edge or the hanging wall of a fault scarp. The wavefield is reflected from the interface, to return to the surface along substantially the same trajectory as the original downgoing wavefield as a refracted reflection. That phenomenon is sometimes known as a diving wave or turning wave. Because the obstruction is seen from below, the dip angle is likely to be substantially greater than the usual 90.degree. limit imposed upon routine data-processing methods.
U.S. Pat. No. 5,138,584, issued Aug. 11, 1992 to Ira D. Hale describes a method for migrating seismic data for formations that are located in geological media that cause seismic waves to be refracted so substantially that the waves turn upward. The method includes the steps of tabulating a first phase shift function as a function of the wave vector and the angular frequency of seismic waves in the geologic media, tabulating a second phase shift function, storing the tabulated values of the first and second phase shift functions, calculating a third phase shift function based upon the first and second phase shift functions and migrating recorded seismic data using the first, second and third phase shift functions.
In a paper presented to the 61st annual meeting of the Society of Exploration Geophysicists in 1991, D. Hale et al. described "Imaging Salt with Turning Seismic Waves" and exhibited examples of steep dip imaging.
The references above cited assumed a constant formation velocity within a plurality of thin layers (dz) and employed phase shift migration to accomplish the desired results. Such migration will result in imaging errors in areas of steep linear velocity gradients or in areas where the vertical velocity function exhibits significant positive curvature. There is a need to provide a method for migration and imaging of overturned dips in such areas as well as to provide a computer-aided processing routine that is economical of computer time.